Public transport in Berlin:
For a one way trip in the inner city you usually need an AB-ticket (2.30 EUR) valid in busses, underground and S-Bahn. Alternatively a 4-trip-AB-ticket (8.20 EUR) or AB day ticket (6.30 EUR) might be cheaper, just depends on the number of trips you do per day (details single-ticket, 4-trip-ticket).

From Airport Schönefeld to the venue (BGBM, Königin-Luise-Platz/Botanischer Garten) you might need a good hour, from Airport Tegel you might need about an hour by public transport (...if the public transport works properly).